HCF and LCM Notes Part-1
If number a divided another
number b exactly, we say that a is a factor of b.
In this case, b is called a multiple of a.
2. Highest Common
Factor (H.C.F.) or Greatest Common Measure (G.C.M.) or Greatest Common Divisor
(G.C.D.):
The H.C.F. of two or more than two numbers is the
greatest number that divided each of them exactly.
There are two methods of finding the H.C.F. of a
given set of numbers:
I. Factorization Method: Express
the each one of the given numbers as the product of prime factors. The product
of least powers of common prime factors gives H.C.F.
II. Division Method: Suppose
we have to find the H.C.F. of two given numbers, divide the larger by the
smaller one. Now, divide the divisor by the remainder. Repeat the process of
dividing the preceding number by the remainder last obtained till zero is
obtained as remainder. The last divisor is required H.C.F.
Finding the H.C.F. of more than two numbers: Suppose we have to find the
H.C.F. of three numbers, then, H.C.F. of [(H.C.F. of any two) and (the third
number)] gives the H.C.F. of three given number.
Similarly, the H.C.F. of more than three numbers
may be obtained.
3. Least Common
Multiple (L.C.M.):
The least number which is exactly divisible by each
one of the given numbers is called their L.C.M.
There are two methods of finding the L.C.M. of a
given set of numbers:
I. Factorization
Method: Resolve each one of the given
numbers into a product of prime factors. Then, L.C.M. is the product of highest
powers of all the factors.
II. Division
Method (short-cut): Arrange
the given numbers in a rwo in any order. Divide by a number which divided
exactly at least two of the given numbers and carry forward the numbers which
are not divisible. Repeat the above process till no two of the numbers are
divisible by the same number except 1. The product of the divisors and the
undivided numbers is the required L.C.M. of the given numbers.
4.
Product of two numbers = Product of their H.C.F.
and L.C.M.
5. Co-primes: Two numbers are said to be
co-primes if their H.C.F. is 1.
6. H.C.F. and
L.C.M. of Fractions:
1. H.C.F. =
|
H.C.F. of
Numerators
|
L.C.M. of
Denominators
|
2. L.C.M. =
|
L.C.M. of
Numerators
|
H.C.F. of
Denominators
|
8. H.C.F. and
L.C.M. of Decimal Fractions:
In a given numbers, make the same number of decimal
places by annexing zeros in some numbers, if necessary. Considering these
numbers without decimal point, find H.C.F. or L.C.M. as the case may be. Now,
in the result, mark off as many decimal places as are there in each of the
given numbers.
9. Comparison of
Fractions:
Find the L.C.M. of the denominators of the given
fractions. Convert each of the fractions into an equivalent fraction with L.C.M
as the denominator, by multiplying both the numerator and denominator by the
same number. The resultant fraction with the greatest numerator is the greatest.
The Above Content is a Clone from IndiaBix.com